On 2010-06-20, Peter Webb <webbfamily@DIESPAMDIEoptusnet.com.au> wrote:> Of course it is computable.>> Cantor provides an explicit algorithm for computing it.

Cantor provides an explicit algorithm for computing it with the list Las input. Look again at the definition of "computable real". Is "thealgorithm may take as input an auxiliary list of infinite many realnumbers" part of that definition?

> I make no mention of finite algorithms. I just do *exactly* the same> construction, but applied to a purported list of all computable> Reals instead of a purported list of all Reals.

The definition of your term "computable real" includes references to"finite algorithm". So you do make reference to a finite algorithm,and Cantor does not.

> Cantor: Lets form an anti-diagonal using this explicit construction> based upon the nth digit of the nth Real on the list. It is> obviously a Real, and it is obviously missing.

Cantor did not make any assumption that it was "obviously" a real. Infact, he went to some trouble to *prove* that it specified a realnumber.

> Peter: Lets form an anti-diagonal using this explicit construction> based upon the nth digit of the nth computable Real on the list. It> is obviously a computable Real, and it is obviously missing.

You, on the other hand, make no effort whatsoever to prove that theantidiagonal number is computable. If you actually did, you would runinto insuperable difficulties.

The devil is in the details in any mathematical proof. You areactively *avoiding* the details and just assuming they work out. Thatrenders your so-called proof invalid, and is exactly why I acceptCantor's and not yours.

At this point, and in this respect, it is clear that you are just asmuch of a crank as JSH and WM.